关键词：SAT数学真题
摘要：数学作为SAT考试中的一个重要部分，它的备考除了掌握大量知识点以外，还要勤加练习，小编为大家整理大量习题，希望对备考的同学有所帮助!
1. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?
A. f(-1)
B. f(0)
C. f(1)
D. f(3)
E. f(4)
2. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?
A. 2.25
B. 3
C. 4
D. 4.5
E. 6
3. If n ≠ 0, which of the following must be greater than n?
I 2n
II n²
III 2 - n
A. I only
B. II only
C. I and II only
D. II and III only
E. None
4. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
A. 20
B. 15
C. 8
D. 5
E. 3.2
5. n and p are integers greater than 1
5n is the square of a number
75np is the cube of a number.
The smallest value for n + p is
A. 14
B. 18
C. 20
D. 30
E. 50
6. If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?
I 6
II 0
III -6
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III
7. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
A. 48
B. 49
C. 50
D. 51
E. 52
8. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?
A. 23
B. 22
C. 18
D. 16
E. 14
9. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
A. 6
B. 8
C. 10
D. 20
E. 40
10. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
A. 11/P + 6
B. P/11 +6
C. 17 - P/6
D. 17/P
E. 11.5P
参考答案及解析：
1.Correct Answer: D
Explanation:
You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.sat
A (-1 + 2) / (-1-2) = -2 / 2 = -1;
B (0 + 2) / (0-2) = 2/ -2 = -1;
C (1 + 2) / (1-2) = 3/-1 = -3;
D (3 + 2) / (3-2) = 5/1 = 5;
E (4+ 2) / (4-2) = 6/2 = 3
If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.
2.Correct Answer: D
Explanation:
(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral 9 - (2 x ½ x 3 x 1.5) = 4.5
3.Correct Answer: E
Explanation:
Remember that n could be positive negative or a fraction. Try out a few cases: In case I, if n is -1, then 2n is less than n. In case II, if n is a fraction such as ½ then n2 will be less than n. In case III, if n is 2, then 2-n = 0, which is less than n. Therefore, none of the choices must be greater than n
4.Correct Answer: C
Explanation:
If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8
5.Correct Answer: A
Explanation:
The smallest value for n such that 5n is a square is 5. 75np can now be written as 75 x 5 x p. This gives prime factors.... 3 x 5 x 5 x 5 x p To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9 n + p = 5 + 9 = 14
6. Correct Answer: A
Explanation:
Choice I is correct because f(x) = 6 when x=3. Choice II is incorrect because to make f(x) = 0, x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x² would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)
7. Correct Answer: C
Explanation:
1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 50
8. Correct Answer: B
Explanation:
First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A + BC = 143. A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 22
9. Correct Answer: B
Explanation:
Total volume of water = 12 liters = 12 x 1000 cm3. The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 8
10. Correct Answer: A
Explanation:
Let Ben’s age now be B. Anita’s age now is A. (A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6). 11/P = B-6
(11/P) + 6 = B